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GEOGRAL

Geometry of Grassmannian Lagrangian manifolds and their submanifolds, with applications to nonlinear partial differential equations of physical interest

Total Cost €

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EC-Contrib. €

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Partnership

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 GEOGRAL project word cloud

Explore the words cloud of the GEOGRAL project. It provides you a very rough idea of what is the project "GEOGRAL" about.

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Project "GEOGRAL" data sheet

The following table provides information about the project.

Coordinator
INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK 

Organization address
address: UL. SNIADECKICH 8
city: WARSZAWA
postcode: 00 956
website: http://www.impan.gov.pl

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Poland [PL]
 Project website https://www.impan.pl/en/sites/gmoreno/home
 Total cost 146˙462 €
 EC max contribution 146˙462 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2014
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2015
 Duration (year-month-day) from 2015-09-01   to  2017-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK PL (WARSZAWA) coordinator 146˙462.00

Map

 Project objective

The aim of GEOGRAL is to strengthen the bonds of the geometric theory of nonlinear PDEs (and, in particular, integrable systems and equations of Monge-Ampère type) with the geometry of Lagrangian Grassmannians and their submanifolds. In spite of the evident parallelism between these two disciplines, attempts have been rare, yet sophisticated, to cast a bridge between them, and the Applicant himself already gave his own contribution in this direction: he clarified the structure of the space of non-maximal integral elements of the contact planes in jet spaces and studied 3rd order Monge-Ampère equations (which turn out to be of key relevance in topological field theories) through the so-called meta-symplectic structure on the 1st prolongation of a contact manifold. GEOGRAL has a wide applicative scope, as its theoretical results can be tested on equations and variational problems of key importance for Natural Sciences, Technology and Economy. Tailored to the Applicant's scientific profile and designed in continuity with his previous and current research activities, GEOGRAL consists of four research lines: [MOV] Regard Lagrangian Grassmannians as homogeneous spaces and and use Cartan's method of moving frame to classify their submanifolds, as in D. The's work, and characterise the corresponding invariant equations, in continuity with D. Alekseevsky's work. [HYD] Continue the study of certain rational normal curve bundles on Lagrangian Grassmannians, and their bisecant varieties, which are associated with integrable systems of hydrodynamic type, discovered by E. Ferapontov. [HMA] Geometric study of multi-dimensional and higher-order Monge-Ampère equations, initiated by G. Manno and the Applicant. [FBV] Study some examples of Cauchy problems and variational problems with free boundary values by exploiting the geometric structures on the spaces of isotropic flags and non-maximal isotropic elements of a meta-symplectic space, in continuity with the Applicant's own work.

 Publications

year authors and title journal last update
List of publications.
2017 A. J. Bruce, K. Grabowska, G. Moreno
On a Geometric Framework for Lagrangian Supermechanics
published pages: , ISSN: 1941-4889, DOI:
Journal of Geometric Mechanics 2019-07-23
2016 Giovanni Moreno, Monika Ewa Stypa
Geometry of the free-sliding Bernoulli beam
published pages: , ISSN: 1804-1388, DOI: 10.1515/cm-2016-0011
communications in mathematics 2 issues/vol./yr. 2019-07-23
2017 Giovanni Moreno
An introduction to completely exceptional 2nd order scalar PDEs
published pages: , ISSN: , DOI:
2019-07-23
2016 Gianni Manno, Giovanni Moreno
Meta-Symplectic Geometry of 3 rd Order Monge-Ampère Equations and their Characteristics
published pages: , ISSN: 1815-0659, DOI: 10.3842/SIGMA.2016.032
Symmetry, Integrability and Geometry: Methods and Applications 2019-07-23
2016 Jan Gutt, Gianni Manno, Giovanni Moreno
Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution
published pages: , ISSN: 0393-0440, DOI: 10.1016/j.geomphys.2016.04.021
Journal of Geometry and Physics 2019-07-23

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